Independent of delay stabilization using implicit Lyapunov function method

International audienceNonlinear implicit Lyapunov function based control algorithms with delay in control and/or measurement channel are presented. The proposed control algorithms provide global asymptotic stability for all delays less than a certain threshold value and global asymptotic stability with respect to a compact set containing the origin for any delay over the threshold value. The algorithms are also applicable for the fast-varying delay and sampled-data cases. The theoretical results are supported by numerical simulations and comparison

Robust Stabilization of Control Affine Systems with Homogeneous Functions

International audienceThe stabilization problem of the affine control system $\dot x = f_0 (x) + u_1 f_1(x)+..+u_m f_m(x)$ with homogeneous functions $f_i$ is studied. This class of systems is of interest due to the robust properties of homogeneity and the fact that many affine systems can be approximated by or transformed to the class under consideration. An advantage of the introduced design method is that the tuning rules are presented in the form of linear matrix inequalities. Performance of the approach is illustrated by a numerical example